Prove that if a sequence of continous functions uniformly converges on [a,b] then the union of their graphs is a null set.
In other words:
Prove that if the sequence converges uniformly on [a,b] then the set : is a null set...

I know the function f is continous ( ) and that the graph of the function f and of each if a null set....
Can't figure out how to prove what I need to prove

Thanks in advance

May 15th 2010, 08:34 PM

dwsmith

Quote:

Originally Posted by WannaBe

Prove that if a sequence of continous functions uniformly converges on [a,b] then the union of their graphs is a null set.
In other words:
Prove that if the sequence converges uniformly on [a,b] then the set : is a null set...

I know the function f is continous ( ) and that the graph of the function f and of each if a null set....
Can't figure out how to prove what I need to prove

Thanks in advance

Try a proof by contradiction.

~

May 16th 2010, 02:21 AM

WannaBe

...

Quote:

Originally Posted by dwsmith

Try a proof by contradiction.

~

If the set A isn't a null set, then there is an such as there is no finite amount of rectangles that cover the set A and their sum is less than .
In other words, we assume by contradiction that there is an such as every finite amount of rectangles that cover the set A- their sum is ...

I've no idea how I can continue from this point... It seems to be very difficult to continue from this point...